$A$ stationary nucleus (mass number = $A$) emits an $\alpha$-particle with velocity $v$. Find the velocity of the daughter nucleus.

$A$ radioactive nucleus emits an $\alpha$-particle to become a stable nucleus. If the velocity of the $\alpha$-particle is $\upsilon$ and the mass number of the original radioactive nucleus is $A$,what will be the velocity of the daughter nucleus?

From the statements given below:
$(A)$ The angular momentum of an electron in $n^{\text{th}}$ orbit is an integral multiple of $\hbar$.
$(B)$ Nuclear forces do not obey inverse square law.
$(C)$ Nuclear forces are spin dependent.
$(D)$ Nuclear forces are central and charge independent.
$(E)$ Stability of nucleus is inversely proportional to the value of packing fraction.
Choose the correct answer from the options given below:

Both the nucleus and the atom of some element are in their respective first excited states. They get de-excited by emitting photons of wavelengths $\lambda_N$ and $\lambda_A$ respectively. The ratio $\frac{\lambda_N}{\lambda_A}$ is closest to

The graph between the number of decayed atoms $N'$ of a radioactive element and time $t$ is:

Match List $I$ of the nuclear processes with List $II$ containing parent nucleus and one of the end products of each process and then select the correct answer using the codes given below the lists:

List $I$	List $II$
$P$. Alpha decay	$1$. ${ }_{8}^{15} O \rightarrow{ }_{7}^{15} N + \dots$
$Q$. $\beta^{+}$ decay	$2$. ${ }_{92}^{238} U \rightarrow{ }_{90}^{234} Th + \dots$
$R$. Fission	$3$. ${ }_{83}^{185} Bi \rightarrow{ }_{82}^{184} Pb + \dots$
$S$. Proton emission	$4$. ${ }_{94}^{239} Pu \rightarrow{ }_{57}^{140} La + \dots$

Codes: $P \quad Q \quad R \quad S$